Question

A needle of a sewing machine moves along a path of amplitude 4 cm with frequency 5 Hz. Find its acceleration 1/30 s after it has crossed the mean position.

Answer 1

Given : A=4 cm = 4 x 10^-2m, η = 5Hz, t= 1/30 s

ω = 2πη = 2π x 5 = 10π rad/s

Therefore, the magnitude of the acceleration,

|a| = ω²x = ω²A sin ωt         

= (10π)² (4 X 10^-2) sin 10π/30

= 4π² sin π/3 = 4 (9.872)(0.866) = 34.20 m/s²